https://doi.org/10.1140/epjc/s10052-017-5304-9
Regular Article - Theoretical Physics
Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories
1
Departamento de Física, Universidade Federal do Piauí, 64049-550, Teresina, PI, Brazil
2
Escola Politécnica de Pernambuco, Universidade de Pernambuco, 50720-001, Recife, PE, Brazil
3
Instituto de Física, Universidade Federal de Alagoas, 57072-900, Maceió, AL, Brazil
* e-mail: prscarvalho@ufpi.edu.br
Received:
14
July
2017
Accepted:
16
October
2017
Published online:
9
November
2017
In this work we evaluate analytically the ultraviolet divergences of Lorentz-violating massive O(N) 
scalar field theories, which are exact in the Lorentz-violating mechanism, firstly explicitly at next-to-leading order and latter at any loop level through an induction procedure based on a theorem following from the exact approach, for computing the corresponding critical exponents. For attaining that goal, we employ three different and independent field-theoretic renormalization group methods. The results found for the critical exponents show that they are identical in the three distinct methods and equal to their Lorentz-invariant counterparts. Furthermore, we show that the results obtained here, based on the single concept of loop order of the referred terms of the corresponding 
-function and anomalous dimensions, reduce to the ones obtained through the earlier non-exact approach based on a joint redefinition of the field and coupling constant of the theory, in the appropriate limit.
© The Author(s), 2017
